The league leaders scored twice in the final 16 minutes at the Estadio Hernando Siles after the visitors had taken an early lead.
Juan Carlos Arce cancelled out Ignacio Garcia's opener before William Ferreira scored a dramatic late winner.
The loss saw Wilstermann drop six points behind Bolivar, while San Jose stayed within three after a 3-0 win over Sport Boys.
Garcia put the visitors ahead in the fourth minute after neat interplay inside the area saw him find space and finish, with his strike going in off the post.
Bolivar equalised with a stunning counter-attack with 16 minutes remaining as Arce was released to finish in a one-on-one.
The hosts found a winner in the second minute of additional time as Ferreira struck in a one-on-one after a fine team move.
San Jose outclassed Sport Boys in a 3-0 win, which came on the back of a first-half brace from Marcelo Gomes.
Carlos Neumann added a header in the second half as San Jose clinched their third straight league win.
Elsewhere, The Strongest and Aurora played out a 0-0 draw and Real Potosi and Club Universitario both clinched 3-0 wins.
Real Potosi left it to the final quarter of an hour to seal their win over Guabira and Club Universitario were far too good for Oriente Petrolero.
